Examples

End-to-end case studies on real, classic functional-data datasets. Each page loads a vendored dataset, runs a genuine fdars analysis, and generates its figures at build time — so the code you read is exactly the code that produced the plots.

The datasets (Berkeley Growth, Canadian Weather, Tecator, Phoneme, Wine, Sonar) live under docs/data/ with sources and licenses documented in the data README; the penicillin batches are synthetic. All are loaded through the small helper docs_data.

Alignment & shape

Growth curve alignment

Berkeley Growth: separate the timing of the pubertal growth spurt from its size with elastic alignment and the Karcher mean.

Sonar: mine vs rock

Does elastic/TSRVF alignment help classify sonar returns? An honest head-to-head against the raw curves.

Representation: Andrews curves

Andrews Wine: why curves?

Turn a 13-dimensional wine table into curves and watch three cultivars separate visually.

Andrews Wine: outliers

Functional depth and the outliergram flag atypical wines among the Andrews curves.

Andrews Wine: clustering

Cluster the curves, compare to the true cultivars, and see which chemical features drive the split.

Andrews Wine: quality control

Treat one cultivar as in-control and flag out-of-spec wines with a functional tolerance view.

Regression & explainability

Predicting fat from NIR spectra

Tecator: scalar-on-function PLS predicts meat fat content, with an interpretable coefficient curve.

Honest model comparison

Out-of-fold cross-validation compares FPC-LM, PLS and NP regression — and exposes optimistic in-sample R².

Recovering predictive regions

Which wavelengths drive the fat prediction? Significant-region and importance tools localize the signal.

Classification

Phoneme recognition

Shape-based classification of five phonemes from their log-periodogram curves, evaluated by cross-validation.

Seasonal & regional analysis

Weather curves: FPCA & clustering

Canadian Weather: FPCA finds the dominant temperature modes and k-means recovers Canada's climate regions.

Annual cycle detection

Recover the ~365-day period, quantify seasonal strength, and decompose a station with STL.

Geographic effects on rainfall

Precipitation profiles by region, with FPCA scores tracking latitude across the country.

Process monitoring

Inline spectra monitoring

Tecator: a T²/SPE control chart flags off-spec spectra and contribution plots localize the fault.

Detection power & false alarms

Trade off detection rate against false-alarm rate as the control limit is tightened.

Penicillin batch monitoring

Monitor fermentation batches (synthetic) and catch faulty batches as their trajectories drift.

What each example shows

Example	Dataset	fdars techniques
Growth curve alignment	Berkeley Growth	deriv_1d, elastic_align_pair, karcher_mean
Sonar: mine vs rock	Sonar	tsrvf_transform, elastic_self_distance_matrix, fclassif_knn
Andrews Wine: why curves?	Wine	Andrews transform, Fdata
Andrews Wine: outliers	Wine	depth, outliergram, magnitude_shape
Andrews Wine: clustering	Wine	kmeans_fd, gmm_cluster, silhouette_score_data
Andrews Wine: quality control	Wine	fpca_tolerance_band / spm
Predicting fat from NIR spectra	Tecator	fregre_pls, predict_fregre_pls, fregre_np
Honest model comparison	Tecator	fregre_cv, model_selection_ncomp
Recovering predictive regions	Tecator	significant_regions, pointwise_importance, functional_pdp
Phoneme recognition	Phoneme	fclassif_knn, fclassif_lda, fclassif_cv
Weather curves: FPCA & clustering	Canadian Weather	fpca, kmeans_fd, silhouette_score_data
Annual cycle detection	Canadian Weather	estimate_period_fft, seasonal_strength, stl_decompose
Geographic effects on rainfall	Canadian Weather	fpca, fosr
Inline spectra monitoring	Tecator	spm_phase1, spm_monitor, hotelling_t2
Detection power & false alarms	Penicillin (synthetic)	spm_phase1, t2_control_limit, arl0_t2
Penicillin batch monitoring	Penicillin (synthetic)	spm_phase1, spm_monitor, t2_pc_contributions

Reproducing locally

Every dataset is loadable outside the docs too:

import sys; sys.path.insert(0, "scripts")
from docs_data import (load_growth, load_canadian_weather, load_tecator,
                       load_phoneme, load_wine, load_sonar, load_penicillin)

age, X, meta = load_growth()          # (argvals, curves, labels)